It is given that line segment CB is parallel to line segment ED and line segment CB is congruent to line segment ED. Angle E is congruent to angle C because parallel lines cut by a transversal produce alternate interior angles. Angle DFE and angle BFC are vertical angles, so then angle DFE is congruent to angle BFC by the vertical angle theorem. So then if triangle CBF were rotated around point F so that angle C coincides with angle E, line segment CB coincide with line segment ED, and angle BFC coincides with angle DFE, triangle CBF is congruent to triangle EDF.